A judge recently assigned to preside over the racketeering and murder case of James “Whitey’’ Bulger said Tuesday that she plans to go forward with the highly anticipated trial in June, drawing cheers from relatives of some of the gangster’s alleged victims who feared there would be a delay.

US District Judge Denise Casper said she will stick to the previously set schedule, with opening statements June 10 in a trial that lawyers estimated would last all summer and probably into September.

Prosecutors said they will call about 50 witnesses. It is ­unclear how many witnesses the defense will call.

Bulger’s lawyers cited concerns about the 83-year-old gangster’s health for the first time when Casper proposed a trial schedule of 9 a.m. to 1 p.m. every day except Wednesdays, when it would be extended to 2:30 p.m.

Bulger’s lawyer, J.W. Carney Jr., said that ­although Bulger is “physically and mentally’’ prepared for his trial, he will have to be awakened very early for his daily two-hour commute from the Plymouth County Correctional Facility to the John ­Joseph Moakley US Courthouse on Boston’s waterfront. He proposed extending the trial day on Fridays, instead of Wednesdays, so Bulger would have the weekend to recuperate.

But Assistant US Attorney Brian T. Kelly said he was more concerned about jurors, who will give up their summer vacations to hear the case and should not be asked to stay late on Fridays. The judge said she will seat 18 jurors, including six alternates.

Bulger, who was captured in Santa Monica, Calif., in June 2011 after more than 16 years on the run, is charged in a sweeping federal racketeering indictment with participating in 19 murders and extorting drug dealers, bookmakers, and legitimate businessmen.

Steve Davis, whose 26-year-old sister Debra was allegedly strangled by Bulger in 1981, said, “Getting up early in the morning shouldn’t affect him. He’s locked up 23 hours a day so he’s got plenty of time to sleep.”

Davis, who has expressed fear that Bulger will die before he stands trial, said he was elated by Casper’s announcement that she will not delay the trial.

Casper, a former federal prosecutor who was appointed to the bench two years ago, said during her first Bulger hearing that she had no history with the case that would require her to recuse herself.

“I had nothing to do with the prosecution of this case,” said Casper, pointing out that she did not start practicing law ­until 1995, the same year that Bulger was indicted on federal racketeering charges and ­became a fugitive.

Bulger’s lawyers raised no objection to Casper’s assignment to the case. She was randomly selected March 14 to replace Judge Richard Stearns, who was ordered to step aside by the US Court of Appeals for the First Circuit because of the public perception that he could not be objective.

Bulger’s lawyers argued for Stearns’s removal because he was a top-ranking prosecutor in the US attorney’s office in the 1980s, during the same period that Bulger says another federal prosecutor, Jeremiah T. O’Sullivan, promised him immunity for all of his crimes, including murder. O’Sullivan died in 2009.

Before being ordered to ­recuse himself, Stearns had ­rejected Bulger’s request to present his immunity assertion to jurors, ruling that O’Sullivan did not have the authority to give Bulger a “license to kill.”

Bulger’s lawyers asked Casper to reconsider their ­request to present the immunity claim to jurors.

Casper said she was not inclined to revisit Stearns’s finding that the government cannot give a defendant prospective immunity, for crimes that have yet to occur.

However, she agreed to ­review briefs on the issue before making a final ruling.

In a series of criminal and civil proceedings, Bulger has been portrayed through testimony and court documents as a longtime FBI informant who was protected by his corrupt handlers because he provided information against his rivals in the Mafia.

However, Bulger insists that he was never an FBI informant.

In a motion filed late Monday, Bulger’s lawyers accused the Justice Department of cultivating inappropriate relationships with other organized crime figures, including hitman Joseph Barboza, Gregory ­Scarpa, and Mark Rossetti from the 1960s to the present, then concealing the nature of those relationships.

They urged the judge to ­order the government to turn over historical documents detail­ing those relationships.

The Justice Department “has fraudulently characterized James Bulger as an informant despite knowing that the ­‘Bulger informant file’ was fabricated,” Bulger’s lawyers wrote.

“This is yet another attempt to silence James Bulger to conceal the existence of his immunity agreement with the [Depart­ment of Justice].”